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Lecture

This

**preview**shows half of the first page. to view the full**2 pages of the document.**Statistics Lecture

September 28, 2011

Statistics and Parameters

•Graphs are limited in what they can tell us

•Difficulty in making inferences about a population when looking

at a subset or sample

•So we need to use numerical measures

•Measures associated with a sample are called statistics

•Parameter [population] and statistics [sample]

Measures of the Centre

•Mean

oMost common measure of central tendency

oIt is the sum of all values divided by the number of

observations

oSample measurement:

•Median: value occupying the ‘middle position’ of an ordered set

of observations

oOrder of the observations, lowest to highest and find the

middle position

o.5(n+1)

oUneven observations: odd number of observations

oEven observations: use the same formula but you’ll have

the add the two and divide it by two

•Mode: value that occurs at the highest frequency

oAllows you to locate the peak of a relative frequency

histogram

Choosing an appropriate measure

•Mean is usually the best but it is not the best when the

distribution is bi-modal and is not good with outliers which skew

the distribution

Measures of Dispersion

•Range: simplest measure

oTakes difference between smallest and largest value in the

dataset

oIs influenced by outliers

oRange= Xmax- Xmin

•Standard Deviation: comparing each value to the mean

•Variance: always represented as S2, n-1 is because you are using

a sample

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